{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python for Finance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Analyze Big Financial Data**\n",
    "\n",
    "O'Reilly (2014)\n",
    "\n",
    "Yves Hilpisch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img style=\"border:0px solid grey;\" src=\"http://hilpisch.com/python_for_finance.png\" alt=\"Python for Finance\" width=\"30%\" align=\"left\" border=\"0\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Buy the book ** |\n",
    "<a href='http://shop.oreilly.com/product/0636920032441.do' target='_blank'>O'Reilly</a> |\n",
    "<a href='http://www.amazon.com/Yves-Hilpisch/e/B00JCYHHJM' target='_blank'>Amazon</a>\n",
    "\n",
    "**All book codes & IPYNBs** |\n",
    "<a href=\"http://oreilly.quant-platform.com\">http://oreilly.quant-platform.com</a>\n",
    "\n",
    "**The Python Quants GmbH** | <a href='http://tpq.io' target='_blank'>http://tpq.io</a>\n",
    "\n",
    "**Contact us** | <a href='mailto:pff@tpq.io'>pff@tpq.io</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stochastics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pylab import plt\n",
    "plt.style.use('seaborn')\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams['font.family'] = 'serif'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Random Numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "uuid": "fba5b184-6652-4665-9053-1741d9b16bb9"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy.random as npr\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "uuid": "8763b99e-6b02-4003-8567-c0f505986e5a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.3470783 ,  0.43883921,  0.23788587,  0.75822653,  0.99009727,\n",
       "        0.13155303,  0.78720349,  0.50878209,  0.56281509,  0.87045611])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npr.rand(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "uuid": "16f2a7c4-62dd-4d0f-bde9-fafb61e0fb64"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.38766647,  0.0554509 ,  0.86512701,  0.91460403,  0.37047273],\n",
       "       [ 0.32913903,  0.69832843,  0.95601918,  0.15324232,  0.41123652],\n",
       "       [ 0.42147484,  0.28321986,  0.1561957 ,  0.70527834,  0.25442396],\n",
       "       [ 0.30560038,  0.34688473,  0.98828291,  0.91984552,  0.60762796],\n",
       "       [ 0.80540565,  0.83123396,  0.56839667,  0.44675888,  0.13949333]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npr.rand(5, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "uuid": "2d14b433-a7da-4aac-a534-56ab4c8a5d84"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.4192794 ,  8.49602036,  6.56474939,  5.61550623,  8.21589491,\n",
       "        9.87441367,  9.71012789,  9.22954444,  7.82770408,  5.9210135 ])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 5.\n",
    "b = 10.\n",
    "npr.rand(10) * (b - a) + a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "uuid": "a05adb2b-5704-4189-b0e8-19318ac3f0b9"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 7.4555587 ,  7.25245467,  6.78044248,  5.12162099,  6.48333077],\n",
       "       [ 7.3901245 ,  8.82639577,  5.27267545,  6.5219321 ,  6.75694889],\n",
       "       [ 7.96328532,  7.55976364,  6.80646059,  6.97177017,  6.97922828],\n",
       "       [ 6.97933894,  7.74085179,  9.37330111,  6.83779434,  7.57556403],\n",
       "       [ 6.13756775,  5.30619929,  9.86039814,  9.98235816,  8.9639068 ]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npr.rand(5, 5) * (b - a) + a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "uuid": "4618b170-6bd3-4500-905a-0fe402f198c1"
   },
   "outputs": [],
   "source": [
    "sample_size = 500\n",
    "rn1 = npr.rand(sample_size, 3)\n",
    "rn2 = npr.randint(0, 10, sample_size)\n",
    "rn3 = npr.sample(size=sample_size)\n",
    "a = [0, 25, 50, 75, 100]\n",
    "rn4 = npr.choice(a, size=sample_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "uuid": "d03c9514-c224-4d2b-ad2a-9285058823b0"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IsFu2bDbq5a3B/Qnw1ezr9YGdge+32iG7Gd8SEfMl7diwqrE5BVKTytTs/0G105zSSSN5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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d18e630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(nrows=2, ncols=2,\n",
    "                                             figsize=(7, 7))\n",
    "ax1.hist(rn1, bins=25, stacked=True)\n",
    "ax1.set_title('rand')\n",
    "ax1.set_ylabel('frequency')\n",
    "ax1.grid(True)\n",
    "ax2.hist(rn2, bins=25)\n",
    "ax2.set_title('randint')\n",
    "ax2.grid(True)\n",
    "ax3.hist(rn3, bins=25)\n",
    "ax3.set_title('sample')\n",
    "ax3.set_ylabel('frequency')\n",
    "ax3.grid(True)\n",
    "ax4.hist(rn4, bins=25)\n",
    "ax4.set_title('choice')\n",
    "ax4.grid(True)\n",
    "# tag: rand_samples\n",
    "# title: Simple pseudo-random numbers\n",
    "# size: 70"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "uuid": "fb2966ea-91ff-49c7-80e6-24bd6162cc5a"
   },
   "outputs": [],
   "source": [
    "sample_size = 500\n",
    "rn1 = npr.standard_normal(sample_size)\n",
    "rn2 = npr.normal(100, 20, sample_size)\n",
    "rn3 = npr.chisquare(df=0.5, size=sample_size)\n",
    "rn4 = npr.poisson(lam=1.0, size=sample_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "uuid": "3f790711-f965-4a10-b3df-47cc85d708d3"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VDSX9I7Aj8HeS9gPOBzaSdALwYeDQNmMzq4WIODUiTo6IOcCtwB0RcR4wl3QhiS8kzZJ2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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d18e208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(nrows=2, ncols=2, figsize=(7, 7))\n",
    "ax1.hist(rn1, bins=25)\n",
    "ax1.set_title('standard normal')\n",
    "ax1.set_ylabel('frequency')\n",
    "ax1.grid(True)\n",
    "ax2.hist(rn2, bins=25)\n",
    "ax2.set_title('normal(100, 20)')\n",
    "ax2.grid(True)\n",
    "ax3.hist(rn3, bins=25)\n",
    "ax3.set_title('chi square')\n",
    "ax3.set_ylabel('frequency')\n",
    "ax3.grid(True)\n",
    "ax4.hist(rn4, bins=25)\n",
    "ax4.set_title('Poisson')\n",
    "ax4.grid(True)\n",
    "# tag: rand_distris\n",
    "# title: Pseudo-random numbers from different distributions\n",
    "# size: 70"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Random Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "uuid": "ac34499c-4675-457e-a0ac-40b8efcdb72e"
   },
   "outputs": [],
   "source": [
    "S0 = 100  # initial value\n",
    "r = 0.05  # constant short rate\n",
    "sigma = 0.25  # constant volatility\n",
    "T = 2.0  # in years\n",
    "I = 10000  # number of random draws\n",
    "ST1 = S0 * np.exp((r - 0.5 * sigma ** 2) * T \n",
    "             + sigma * np.sqrt(T) * npr.standard_normal(I))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "uuid": "7fc0b66a-9ce3-4c5e-bb99-d5e0363a6678"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d188e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(ST1, bins=50)\n",
    "plt.xlabel('index level')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: gbm_T_sn\n",
    "# title: Simulated geometric Brownian motion (via +standard_normal+)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "uuid": "c37a0783-81b1-449f-924e-f792ba5017aa"
   },
   "outputs": [],
   "source": [
    "ST2 = S0 * npr.lognormal((r - 0.5 * sigma ** 2) * T,\n",
    "                        sigma * np.sqrt(T), size=I)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "uuid": "fea07d0c-7fc1-4ab8-8b21-fc36e73c3151"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x115e734a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(ST2, bins=50)\n",
    "plt.xlabel('index level')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: gbm_T_ln\n",
    "# title: Simulated geometric Brownian motion (via +lognormal+)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "uuid": "e5e17dcf-21f4-42ee-bcec-21103aaa8bb3"
   },
   "outputs": [],
   "source": [
    "import scipy.stats as scs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "uuid": "d6f800c9-f38f-4fe1-8cb5-fe9253f1194c"
   },
   "outputs": [],
   "source": [
    "def print_statistics(a1, a2):\n",
    "    ''' Prints selected statistics.\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    a1, a2 : ndarray objects\n",
    "        results object from simulation\n",
    "    '''\n",
    "    sta1 = scs.describe(a1)\n",
    "    sta2 = scs.describe(a2)\n",
    "    print(\"%14s %14s %14s\" % \n",
    "        ('statistic', 'data set 1', 'data set 2'))\n",
    "    print(45 * \"-\")\n",
    "    print(\"%14s %14.3f %14.3f\" % ('size', sta1[0], sta2[0]))\n",
    "    print(\"%14s %14.3f %14.3f\" % ('min', sta1[1][0], sta2[1][0]))\n",
    "    print(\"%14s %14.3f %14.3f\" % ('max', sta1[1][1], sta2[1][1]))\n",
    "    print(\"%14s %14.3f %14.3f\" % ('mean', sta1[2], sta2[2]))\n",
    "    print(\"%14s %14.3f %14.3f\" % ('std', np.sqrt(sta1[3]), np.sqrt(sta2[3])))\n",
    "    print(\"%14s %14.3f %14.3f\" % ('skew', sta1[4], sta2[4]))\n",
    "    print(\"%14s %14.3f %14.3f\" % ('kurtosis', sta1[5], sta2[5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "uuid": "980679e8-56af-49e3-85f3-4b4d1ed90312"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     statistic     data set 1     data set 2\n",
      "---------------------------------------------\n",
      "          size      10000.000      10000.000\n",
      "           min         26.415         29.419\n",
      "           max        350.758        357.693\n",
      "          mean        110.213        110.790\n",
      "           std         40.106         40.480\n",
      "          skew          1.115          1.070\n",
      "      kurtosis          2.155          1.861\n"
     ]
    }
   ],
   "source": [
    "print_statistics(ST1, ST2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stochastic Processes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Geometric Brownian Motion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "uuid": "a6b64214-0041-49cb-b7a8-7b4965d1d03a"
   },
   "outputs": [],
   "source": [
    "I = 10000\n",
    "M = 50\n",
    "dt = T / M\n",
    "S = np.zeros((M + 1, I))\n",
    "S[0] = S0\n",
    "for t in range(1, M + 1):\n",
    "    S[t] = S[t - 1] * np.exp((r - 0.5 * sigma ** 2) * dt \n",
    "            + sigma * np.sqrt(dt) * npr.standard_normal(I))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "uuid": "969180df-b1f3-4f6d-8ec6-21cadbec06f1"
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYkAAAEFCAYAAAAWrxseAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115d35e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(S[-1], bins=50)\n",
    "plt.xlabel('index level')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: gbm_dt_hist\n",
    "# title: Simulated geometric Brownian motion at maturity\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "uuid": "37d83fc1-6b2d-4d94-a5d1-75d2ba569283"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     statistic     data set 1     data set 2\n",
      "---------------------------------------------\n",
      "          size      10000.000      10000.000\n",
      "           min         28.630         29.419\n",
      "           max        388.412        357.693\n",
      "          mean        111.159        110.790\n",
      "           std         40.165         40.480\n",
      "          skew          1.108          1.070\n",
      "      kurtosis          2.009          1.861\n"
     ]
    }
   ],
   "source": [
    "print_statistics(S[-1], ST2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "uuid": "c424f261-aa3f-4b04-9b5d-bb6824107fa0"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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1G5/rifwmgnw9SB6NePLUqokJ8SEmZCSyar4VenQlslKQuW/o6higKNdISlbY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0EQPg+ERFH8hyAIpUC1KIoeQRC+CkwRRfGL5/tsOByRhzsp2JVO1TPP0vjmKsb+138S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\n4pK9BJVblgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115d35b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(S[:, :10], lw=1.5)\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('index level')\n",
    "plt.grid(True)\n",
    "# tag: gbm_dt_paths\n",
    "# title: Simulated geometric Brownian motion paths\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Square-Root Diffusion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "uuid": "b00481e7-074a-4d04-a65d-4ee95f971116"
   },
   "outputs": [],
   "source": [
    "x0 = 0.05\n",
    "kappa = 3.0\n",
    "theta = 0.02\n",
    "sigma = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "uuid": "e085f53a-d065-424e-b1f4-d41c64464c2a"
   },
   "outputs": [],
   "source": [
    "I = 10000\n",
    "M = 50\n",
    "dt = T / M\n",
    "def srd_euler():\n",
    "    xh = np.zeros((M + 1, I))\n",
    "    x1 = np.zeros_like(xh)\n",
    "    xh[0] = x0\n",
    "    x1[0] = x0\n",
    "    for t in range(1, M + 1):\n",
    "        xh[t] = (xh[t - 1]\n",
    "              + kappa * (theta - np.maximum(xh[t - 1], 0)) * dt\n",
    "              + sigma * np.sqrt(np.maximum(xh[t - 1], 0)) * np.sqrt(dt)  \n",
    "              * npr.standard_normal(I))\n",
    "    x1 = np.maximum(xh, 0)\n",
    "    return x1\n",
    "x1 = srd_euler()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "uuid": "93283652-414e-4773-99ca-00e0b24cc088"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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wxY72cuRwIHBtk/VJkn5Wk3cfHQr8PfBl4PPAI4ALgdOAd0bEAcD+wDqAzLwpIj4fERso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\n+X9AoyCgIMxR4QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115993e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x1[-1], bins=50)\n",
    "plt.xlabel('value')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: srd_hist_Euler\n",
    "# title: Simulated square-root diffusion at maturity (Euler scheme)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "uuid": "59c2b6b1-7c7d-44bd-8ae3-8ad16dd2eb30"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6rRqjQeaVEyM4XWampkyARj4dKHv8bC3ELDUNLhxOE50d43PbKiwGskWNdFHG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\nBViCYeSR8QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1156e8860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x1[:, :10], lw=1.5)\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('index level')\n",
    "plt.grid(True)\n",
    "# tag: srd_dt_Euler\n",
    "# title: Simulated square-root diffusion paths (Euler scheme)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "uuid": "b901c93e-a4a9-4f8f-98d9-69754cb586bf"
   },
   "outputs": [],
   "source": [
    "def srd_exact():\n",
    "    x2 = np.zeros((M + 1, I))\n",
    "    x2[0] = x0\n",
    "    for t in range(1, M + 1):\n",
    "        df = 4 * theta * kappa / sigma ** 2\n",
    "        c = (sigma ** 2 * (1 - np.exp(-kappa * dt))) / (4 * kappa)\n",
    "        nc = np.exp(-kappa * dt) / c * x2[t - 1] \n",
    "        x2[t] = c * npr.noncentral_chisquare(df, nc, size=I)\n",
    "    return x2\n",
    "x2 = srd_exact()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "uuid": "98648791-2251-4313-baef-e65e4f3ea059"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KoSBJqhgKkqSKoSBJqhgKkqSKoSBJqjR2R3NE7AOcA/xfimc8P5SZ74uIvYAR4F5gX2Bt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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1156fb1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x2[-1], bins=50)\n",
    "plt.xlabel('value')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: srd_hist_exact\n",
    "# title: Simulated square-root diffusion at maturity (exact scheme)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "uuid": "3d998e1a-e225-4de8-b09b-abf8651d30cb"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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R7mn3H20aJCHLbK3KmXH9FYXpPFCdh4CAo8jGW8e7+fufHuHrjx9jz+neeQsD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\nrUlp3S5dAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1156e6fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x2[:, :10], lw=1.5)\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('index level')\n",
    "plt.grid(True)\n",
    "# tag: srd_dt_exact\n",
    "# title: Simulated square-root diffusion paths (exact scheme)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "uuid": "fc247695-7a20-4452-8c74-96ace26f2ebe"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     statistic     data set 1     data set 2\n",
      "---------------------------------------------\n",
      "          size      10000.000      10000.000\n",
      "           min          0.004          0.005\n",
      "           max          0.051          0.051\n",
      "          mean          0.020          0.020\n",
      "           std          0.006          0.006\n",
      "          skew          0.558          0.602\n",
      "      kurtosis          0.494          0.508\n"
     ]
    }
   ],
   "source": [
    "print_statistics(x1[-1], x2[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "uuid": "7f49cc7d-5264-459c-a9b7-d602daed9f2b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 743 ms, sys: 140 ms, total: 883 ms\n",
      "Wall time: 922 ms\n"
     ]
    }
   ],
   "source": [
    "I = 250000\n",
    "%time x1 = srd_euler()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "uuid": "ede482c4-ec2c-43e2-8128-0c97b44469bd"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.68 s, sys: 19.3 ms, total: 1.7 s\n",
      "Wall time: 1.71 s\n"
     ]
    }
   ],
   "source": [
    "%time x2 = srd_exact()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "uuid": "84a26be5-eede-4478-9f67-c6a97f9804f9"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     statistic     data set 1     data set 2\n",
      "---------------------------------------------\n",
      "          size     250000.000     250000.000\n",
      "           min          0.002          0.004\n",
      "           max          0.066          0.057\n",
      "          mean          0.020          0.020\n",
      "           std          0.006          0.006\n",
      "          skew          0.544          0.573\n",
      "      kurtosis          0.444          0.472\n"
     ]
    }
   ],
   "source": [
    "print_statistics(x1[-1], x2[-1])\n",
    "x1 = 0.0; x2 = 0.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Stochastic Volatility"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "uuid": "786bc4c9-bff7-4a6d-9ae5-1f62c1813518"
   },
   "outputs": [],
   "source": [
    "S0 = 100.\n",
    "r = 0.05\n",
    "v0 = 0.1\n",
    "kappa = 3.0\n",
    "theta = 0.25\n",
    "sigma = 0.1\n",
    "rho = 0.6\n",
    "T = 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "uuid": "0db5ac22-1065-4fd5-92a8-3ccb0780d34c"
   },
   "outputs": [],
   "source": [
    "corr_mat = np.zeros((2, 2))\n",
    "corr_mat[0, :] = [1.0, rho]\n",
    "corr_mat[1, :] = [rho, 1.0]\n",
    "cho_mat = np.linalg.cholesky(corr_mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "uuid": "41b7d810-38b5-4831-bb66-84a57c97415b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1. ,  0. ],\n",
       "       [ 0.6,  0.8]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cho_mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "uuid": "b16ca288-23eb-463b-9b63-4765eea564f9"
   },
   "outputs": [],
   "source": [
    "M = 50\n",
    "I = 10000\n",
    "ran_num = npr.standard_normal((2, M + 1, I))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "uuid": "e7ae274e-fec0-43f5-a171-0dd5f131e6c2"
   },
   "outputs": [],
   "source": [
    "dt = T / M\n",
    "v = np.zeros_like(ran_num[0])\n",
    "vh = np.zeros_like(v)\n",
    "v[0] = v0\n",
    "vh[0] = v0\n",
    "for t in range(1, M + 1):\n",
    "    ran = np.dot(cho_mat, ran_num[:, t, :])\n",
    "    vh[t] = (vh[t - 1] + kappa * (theta - np.maximum(vh[t - 1], 0)) * dt\n",
    "          + sigma * np.sqrt(np.maximum(vh[t - 1], 0)) * np.sqrt(dt)  \n",
    "          * ran[1])\n",
    "v = np.maximum(vh, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "uuid": "0016d6a1-4c5c-4617-847a-d0d1510c3fb9"
   },
   "outputs": [],
   "source": [
    "S = np.zeros_like(ran_num[0])\n",
    "S[0] = S0\n",
    "for t in range(1, M + 1):\n",
    "    ran = np.dot(cho_mat, ran_num[:, t, :])\n",
    "    S[t] = S[t - 1] * np.exp((r - 0.5 * v[t]) * dt +\n",
    "                    np.sqrt(v[t]) * ran[0] * np.sqrt(dt))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "uuid": "5db99fd6-5e32-4c1f-8186-fe6ac910b0c8"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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RtqgkSZKa1Gwy81BmXgz8HiAzfwg83raoJEmSmtRsMvOi6u+VABGxITD0Vm1JkqSOa3bM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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1156e5208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(9, 5))\n",
    "ax1.hist(S[-1], bins=50)\n",
    "ax1.set_xlabel('index level')\n",
    "ax1.set_ylabel('frequency')\n",
    "ax1.grid(True)\n",
    "ax2.hist(v[-1], bins=50)\n",
    "ax2.set_xlabel('volatility')\n",
    "ax2.grid(True)\n",
    "# tag: sv_hist\n",
    "# title: Simulated stochastic volatility model at maturity\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "uuid": "0b542695-d86d-47d9-8be4-760cd9a7786b"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZKhVK7iu9C2fAxY7mvaN6zNHOE3R6uriz6LaYd9/ITsyk0JzP/vajTJfqW31+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\nDICSJEnSsCQDoCRJkjQs/X9PzZaflGDmaQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a18bd4da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, figsize=(7, 6))\n",
    "ax1.plot(S[:, :10], lw=1.5)\n",
    "ax1.set_ylabel('index level')\n",
    "ax1.grid(True)\n",
    "ax2.plot(v[:, :10], lw=1.5)\n",
    "ax2.set_xlabel('time')\n",
    "ax2.set_ylabel('volatility')\n",
    "ax2.grid(True)\n",
    "# tag: sv_paths\n",
    "# title: Simulated stochastic volatility model paths\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "uuid": "398e803e-e0d8-4bc1-9c2a-53ad78cf524d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     statistic     data set 1     data set 2\n",
      "---------------------------------------------\n",
      "          size      10000.000      10000.000\n",
      "           min         16.409          0.175\n",
      "           max        622.522          0.329\n",
      "          mean        107.634          0.243\n",
      "           std         52.475          0.020\n",
      "          skew          1.893          0.154\n",
      "      kurtosis          7.215         -0.007\n"
     ]
    }
   ],
   "source": [
    "print_statistics(S[-1], v[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Jump-Diffusion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "uuid": "4d34dbf3-196e-4125-a11d-f967982540e2"
   },
   "outputs": [],
   "source": [
    "S0 = 100.\n",
    "r = 0.05\n",
    "sigma = 0.2\n",
    "lamb = 0.75\n",
    "mu = -0.6\n",
    "delta = 0.25\n",
    "T = 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "uuid": "b22527e8-afc1-4c69-8253-4e8b6a64f0da"
   },
   "outputs": [],
   "source": [
    "M = 50\n",
    "I = 10000\n",
    "dt = T / M\n",
    "rj = lamb * (np.exp(mu + 0.5 * delta ** 2) - 1)\n",
    "S = np.zeros((M + 1, I))\n",
    "S[0] = S0\n",
    "sn1 = npr.standard_normal((M + 1, I))\n",
    "sn2 = npr.standard_normal((M + 1, I))\n",
    "poi = npr.poisson(lamb * dt, (M + 1, I))\n",
    "for t in range(1, M + 1, 1):\n",
    "    S[t] = S[t - 1] * (np.exp((r - rj - 0.5 * sigma ** 2) * dt\n",
    "                       + sigma * np.sqrt(dt) * sn1[t])\n",
    "                       + (np.exp(mu + delta * sn2[t]) - 1)\n",
    "                       * poi[t])\n",
    "    S[t] = np.maximum(S[t], 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "uuid": "19508067-6759-4e88-9276-0d21a0be9e8e"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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rvDp99dEyYD5AROwG3JGZa4DlwJ4RMTL+MB+4qsO1SdK011goRMTrgKOAF0XERyNiG+A8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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a18c5a4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(S[-1], bins=50)\n",
    "plt.xlabel('value')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: jd_hist\n",
    "# title: Simulated jump diffusion at maturity\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "uuid": "27046a97-3c3c-4265-bde7-45f9b71dc001"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PH45BD2pRi0KuQCYXkMsEZHIZMpmAQilDo1Wi1SnRaJVodCo0GgUnj7Si1Sl5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\n4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BhJsvG9Nt7a08p/P1eP02ZErvCw61A3ZqOej11bx+plpegnoPDPdA5gkzRtlDb7OCPL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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a2c891f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(S[:, :10], lw=1.5)\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('index level')\n",
    "plt.grid(True)\n",
    "# tag: jd_paths\n",
    "# title: Simulated jump diffusion paths\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variance Reduction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "uuid": "293a9f5c-7ae1-4994-b11d-64ba5312559a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Mean  Std. Deviation\n",
      "-------------------------------\n",
      "-0.011870394558  1.008752430725\n",
      "-0.002815667298  1.002729536352\n",
      "-0.003847776704  1.000594044165\n",
      "-0.003058113374  1.001086345326\n",
      "-0.001685126538  1.001630849589\n",
      "-0.001175212007  1.001347684642\n",
      "-0.000803969036  1.000159081432\n",
      "-0.000601970954  0.999506522127\n",
      "-0.000147787693  0.999571756099\n",
      "-0.000313035581  0.999646153704\n",
      "-0.000178447061  0.999677277878\n",
      " 0.000096501709  0.999684346792\n",
      "-0.000135677013  0.999823841902\n",
      "-0.000015726986  0.999906493379\n",
      "-0.000039368519  1.000063091949\n"
     ]
    }
   ],
   "source": [
    "print(\"%15s %15s\" % ('Mean', 'Std. Deviation'))\n",
    "print(31 * \"-\")\n",
    "for i in range(1, 31, 2):\n",
    "    npr.seed(1000)\n",
    "    sn = npr.standard_normal(i ** 2 * 10000)\n",
    "    print(\"%15.12f %15.12f\" % (sn.mean(), sn.std()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "uuid": "5940d5f7-72ed-4fd2-8a48-d66c2d5e45db"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8410000"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i ** 2 * 10000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "uuid": "732f2ba4-3133-4508-92a1-10ee47519f36"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000,)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sn = npr.standard_normal(int(10000 / 2))\n",
    "sn = np.concatenate((sn, -sn))\n",
    "np.shape(sn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "uuid": "3f166fbb-ed57-403f-b251-1b5579ec261d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Mean  Std. Deviation\n",
      "-------------------------------\n",
      " 0.000000000000  1.009653753942\n",
      "-0.000000000000  1.000413716783\n",
      " 0.000000000000  1.002925061201\n",
      "-0.000000000000  1.000755212673\n",
      " 0.000000000000  1.001636910076\n",
      "-0.000000000000  1.000726758438\n",
      "-0.000000000000  1.001621265149\n",
      " 0.000000000000  1.001203722778\n",
      "-0.000000000000  1.000556669784\n",
      "-0.000000000000  1.000113464185\n",
      "-0.000000000000  0.999435175324\n",
      "-0.000000000000  0.999356961431\n",
      "-0.000000000000  0.999641436845\n",
      "-0.000000000000  0.999642768905\n",
      "-0.000000000000  0.999638303451\n"
     ]
    }
   ],
   "source": [
    "print(\"%15s %15s\" % ('Mean', 'Std. Deviation'))\n",
    "print(31 * \"-\")\n",
    "for i in range(1, 31, 2):\n",
    "    npr.seed(1000)\n",
    "    sn = npr.standard_normal(i ** 2 * int(10000 / 2))\n",
    "    sn = np.concatenate((sn, -sn))\n",
    "    print(\"%15.12f %15.12f\" % (sn.mean(), sn.std()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "uuid": "de17794f-4dfd-4441-8d0f-bd097ac0da2c"
   },
   "outputs": [],
   "source": [
    "sn = npr.standard_normal(10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "uuid": "0251bf81-b4d8-4828-80be-9ff972204d06"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.001165998295162494"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sn.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "uuid": "a59c5234-0398-4260-9bcb-d63cd6a7c917"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99125592020460496"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sn.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "uuid": "699ea494-9c78-4ddc-b153-ce291039f77e"
   },
   "outputs": [],
   "source": [
    "sn_new = (sn - sn.mean()) / sn.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "uuid": "e5836915-236c-4c1b-9012-20fb52e50608"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.3803181647963357e-17"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sn_new.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "uuid": "5113ce74-07a2-4b16-b8d0-7ed9495ccb9b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99999999999999989"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sn_new.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "uuid": "f566cd19-61d3-4c69-9391-cb1c906d23c3"
   },
   "outputs": [],
   "source": [
    "def gen_sn(M, I, anti_paths=True, mo_match=True):\n",
    "    ''' Function to generate random numbers for simulation.\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    M : int\n",
    "        number of time intervals for discretization\n",
    "    I : int\n",
    "        number of paths to be simulated\n",
    "    anti_paths: boolean\n",
    "        use of antithetic variates\n",
    "    mo_math : boolean\n",
    "        use of moment matching\n",
    "    '''\n",
    "    if anti_paths is True:\n",
    "        sn = npr.standard_normal((M + 1, int(I / 2)))\n",
    "        sn = np.concatenate((sn, -sn), axis=1)\n",
    "    else:\n",
    "        sn = npr.standard_normal((M + 1, I))\n",
    "    if mo_match is True:\n",
    "        sn = (sn - sn.mean()) / sn.std()\n",
    "    return sn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Valuation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### European Options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "uuid": "693f44be-b3dd-4820-9610-a127f0e9b31b"
   },
   "outputs": [],
   "source": [
    "S0 = 100.\n",
    "r = 0.05\n",
    "sigma = 0.25\n",
    "T = 1.0\n",
    "I = 50000\n",
    "def gbm_mcs_stat(K):\n",
    "    ''' Valuation of European call option in Black-Scholes-Merton\n",
    "    by Monte Carlo simulation (of index level at maturity)\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    K : float\n",
    "        (positive) strike price of the option\n",
    "    \n",
    "    Returns\n",
    "    =======\n",
    "    C0 : float\n",
    "        estimated present value of European call option\n",
    "    '''\n",
    "    sn = gen_sn(1, I)\n",
    "    # simulate index level at maturity\n",
    "    ST = S0 * np.exp((r - 0.5 * sigma ** 2) * T \n",
    "                 + sigma * np.sqrt(T) * sn[1])\n",
    "    # calculate payoff at maturity\n",
    "    hT = np.maximum(ST - K, 0)\n",
    "    # calculate MCS estimator\n",
    "    C0 = np.exp(-r * T) * 1 / I * np.sum(hT)\n",
    "    return C0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "uuid": "f325da52-3e45-4e9e-a4a2-067efb1c3bb7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.044221852841922"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gbm_mcs_stat(K=105.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "uuid": "511974d5-5ceb-4b68-bf7f-e01eaa43f7c6"
   },
   "outputs": [],
   "source": [
    "M = 50\n",
    "def gbm_mcs_dyna(K, option='call'):\n",
    "    ''' Valuation of European options in Black-Scholes-Merton\n",
    "    by Monte Carlo simulation (of index level paths)\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    K : float\n",
    "        (positive) strike price of the option\n",
    "    option : string\n",
    "        type of the option to be valued ('call', 'put')\n",
    "    \n",
    "    Returns\n",
    "    =======\n",
    "    C0 : float\n",
    "        estimated present value of European call option\n",
    "    '''\n",
    "    dt = T / M\n",
    "    # simulation of index level paths\n",
    "    S = np.zeros((M + 1, I))\n",
    "    S[0] = S0\n",
    "    sn = gen_sn(M, I)\n",
    "    for t in range(1, M + 1):\n",
    "        S[t] = S[t - 1] * np.exp((r - 0.5 * sigma ** 2) * dt \n",
    "                + sigma * np.sqrt(dt) * sn[t])\n",
    "    # case-based calculation of payoff\n",
    "    if option == 'call':\n",
    "        hT = np.maximum(S[-1] - K, 0)\n",
    "    else:\n",
    "        hT = np.maximum(K - S[-1], 0)\n",
    "    # calculation of MCS estimator\n",
    "    C0 = np.exp(-r * T) * 1 / I * np.sum(hT)\n",
    "    return C0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "uuid": "44ae2961-ec7c-4e69-b6ff-17b8093a894b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.9500085250284336"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gbm_mcs_dyna(K=110., option='call')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "uuid": "bedb79ae-4f01-41ea-b16a-22ea9781fc0e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12.629934942682004"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gbm_mcs_dyna(K=110., option='put')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "uuid": "e9e52ba0-6ccb-46df-a089-49505d6c7919"
   },
   "outputs": [],
   "source": [
    "from bsm_functions import bsm_call_value\n",
    "stat_res = []\n",
    "dyna_res = []\n",
    "anal_res = []\n",
    "k_list = np.arange(80., 120.1, 5.)\n",
    "np.random.seed(200000)\n",
    "for K in k_list:\n",
    "    stat_res.append(gbm_mcs_stat(K))\n",
    "    dyna_res.append(gbm_mcs_dyna(K))\n",
    "    anal_res.append(bsm_call_value(S0, K, T, r, sigma))\n",
    "stat_res = np.array(stat_res)\n",
    "dyna_res = np.array(dyna_res)\n",
    "anal_res = np.array(anal_res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "uuid": "3f9f44ec-47de-4891-bf82-2b620c647c9a"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZccfV9/a33baawoys0CGSP9K+ep2Z9QKiwDzgGqATcGV9I/LDoOfopTblODPS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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a2d950748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, figsize=(8, 6))\n",
    "ax1.plot(k_list, anal_res, 'b', label='analytical')\n",
    "ax1.plot(k_list, stat_res, 'ro', label='static')\n",
    "ax1.set_ylabel('European call option value')\n",
    "ax1.grid(True)\n",
    "ax1.legend(loc=0)\n",
    "ax1.set_ylim(ymin=0)\n",
    "wi = 1.0\n",
    "ax2.bar(k_list - wi / 2, (anal_res - stat_res) / anal_res * 100, wi)\n",
    "ax2.set_xlabel('strike')\n",
    "ax2.set_ylabel('difference in %')\n",
    "ax2.set_xlim(left=75, right=125)\n",
    "ax2.grid(True)\n",
    "# tag: opt_val_comp_1\n",
    "# title: Comparsion of static and dynamic Monte Carlo estimator values\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "uuid": "3f9f44ec-47de-4891-bf82-2b620c647c9a"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tMHoAADCzI4G7CLYAXgJsDJSGVb+IhKu0/zEsA/JHjiAyZzbRxA6Gp/Xvx0lr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\nVkBOAMzMzAroL/Zz4h9VqpwyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a2c78ada0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, figsize=(8, 6))\n",
    "ax1.plot(k_list, anal_res, 'b', label='analytical')\n",
    "ax1.plot(k_list, dyna_res, 'ro', label='dynamic')\n",
    "ax1.set_ylabel('European call option value')\n",
    "ax1.grid(True)\n",
    "ax1.legend(loc=0)\n",
    "ax1.set_ylim(ymin=0)\n",
    "wi = 1.0\n",
    "ax2.bar(k_list - wi / 2, (anal_res - dyna_res) / anal_res * 100, wi)\n",
    "ax2.set_xlabel('strike')\n",
    "ax2.set_ylabel('difference in %')\n",
    "ax2.set_xlim(left=75, right=125)\n",
    "ax2.grid(True)\n",
    "# tag: opt_val_comp_2\n",
    "# title: Comparsion of static and dynamic Monte Carlo estimator values\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### American Options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "uuid": "033296d5-230b-4b35-ae3f-a2a7ed8c8937"
   },
   "outputs": [],
   "source": [
    "def gbm_mcs_amer(K, option='call'):\n",
    "    ''' Valuation of American option in Black-Scholes-Merton\n",
    "    by Monte Carlo simulation by LSM algorithm\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    K : float\n",
    "        (positive) strike price of the option\n",
    "    option : string\n",
    "        type of the option to be valued ('call', 'put')\n",
    "    \n",
    "    Returns\n",
    "    =======\n",
    "    C0 : float\n",
    "        estimated present value of European call option\n",
    "    '''\n",
    "    dt = T / M\n",
    "    df = np.exp(-r * dt)\n",
    "    # simulation of index levels\n",
    "    S = np.zeros((M + 1, I))\n",
    "    S[0] = S0\n",
    "    sn = gen_sn(M, I)\n",
    "    for t in range(1, M + 1):\n",
    "        S[t] = S[t - 1] * np.exp((r - 0.5 * sigma ** 2) * dt \n",
    "                + sigma * np.sqrt(dt) * sn[t])\n",
    "    # case based calculation of payoff\n",
    "    if option == 'call':\n",
    "        h = np.maximum(S - K, 0)\n",
    "    else:\n",
    "        h = np.maximum(K - S, 0)\n",
    "    # LSM algorithm\n",
    "    V = np.copy(h)\n",
    "    for t in range(M - 1, 0, -1):\n",
    "        reg = np.polyfit(S[t], V[t + 1] * df, 7)\n",
    "        C = np.polyval(reg, S[t])\n",
    "        V[t] = np.where(C > h[t], V[t + 1] * df, h[t])\n",
    "    # MCS estimator\n",
    "    C0 = df * 1 / I * np.sum(V[1])\n",
    "    return C0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "uuid": "18dba6e2-2a7f-4474-bbee-227f354fcbc3"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.7789332794493156"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gbm_mcs_amer(110., option='call')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "uuid": "a82c68fc-9820-43a7-8302-3ae0f5a47650"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.614023206242445"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gbm_mcs_amer(110., option='put')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "uuid": "2c4a0f35-5a41-416b-aa39-53d78d1cc366"
   },
   "outputs": [],
   "source": [
    "euro_res = []\n",
    "amer_res = []\n",
    "k_list = np.arange(80., 120.1, 5.)\n",
    "for K in k_list:\n",
    "    euro_res.append(gbm_mcs_dyna(K, 'put'))\n",
    "    amer_res.append(gbm_mcs_amer(K, 'put'))\n",
    "euro_res = np.array(euro_res)\n",
    "amer_res = np.array(amer_res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "uuid": "6304932d-114f-43b1-ae59-4b0ad2de33fc"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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X7LpEJL1UV8MHH2TyxBNRnn02i+Li4Bp8nz5VDBlSwbHHVrLZZrrvLrIuwrjY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\nMINekqSGGfSSJDXMoJckqWE/Q222G95gyhQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a18c5a7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, figsize=(8, 6))\n",
    "ax1.plot(k_list, euro_res, 'b', label='European put')\n",
    "ax1.plot(k_list, amer_res, 'ro', label='American put')\n",
    "ax1.set_ylabel('call option value')\n",
    "ax1.grid(True)\n",
    "ax1.legend(loc=0)\n",
    "wi = 1.0\n",
    "ax2.bar(k_list - wi / 2, (amer_res - euro_res) / euro_res * 100, wi)\n",
    "ax2.set_xlabel('strike')\n",
    "ax2.set_ylabel('early exercise premium in %')\n",
    "ax2.set_xlim(left=75, right=125)\n",
    "ax2.grid(True)\n",
    "# tag: opt_euro_amer\n",
    "# title: Comparsion of European and LSM Monte Carlo estimator values\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Risk Measures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Value-at-Risk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "uuid": "5473289e-2301-40fb-a665-2d33d43ea09a"
   },
   "outputs": [],
   "source": [
    "S0 = 100\n",
    "r = 0.05\n",
    "sigma = 0.25\n",
    "T = 30 / 365.\n",
    "I = 10000\n",
    "ST = S0 * np.exp((r - 0.5 * sigma ** 2) * T \n",
    "             + sigma * np.sqrt(T) * npr.standard_normal(I))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "uuid": "b2eed114-77e7-479b-b20b-d36a0ffbe636"
   },
   "outputs": [],
   "source": [
    "R_gbm = np.sort(ST - S0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "uuid": "b53e5254-96cc-4294-8ef7-76a2cf21cbca"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a2c6c24a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(R_gbm, bins=50)\n",
    "plt.xlabel('absolute return')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: var_hist_gbm\n",
    "# title: Absolute returns of geometric Brownian motion (30d)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "uuid": "768aa308-d5c2-4f5d-9936-c19c9321996a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence Level    Value-at-Risk\n",
      "---------------------------------\n",
      "           99.99           26.072\n",
      "           99.90           20.175\n",
      "           99.00           15.753\n",
      "           97.50           13.265\n",
      "           95.00           11.298\n",
      "           90.00            8.942\n"
     ]
    }
   ],
   "source": [
    "percs = [0.01, 0.1, 1., 2.5, 5.0, 10.0]\n",
    "var = scs.scoreatpercentile(R_gbm, percs)\n",
    "print(\"%16s %16s\" % ('Confidence Level', 'Value-at-Risk'))\n",
    "print(33 * \"-\")\n",
    "for pair in zip(percs, var):\n",
    "    print(\"%16.2f %16.3f\" % (100 - pair[0], -pair[1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "uuid": "b9952498-c4ad-4d5a-8d3c-3bce1d71006d"
   },
   "outputs": [],
   "source": [
    "dt = 30. / 365 / M\n",
    "rj = lamb * (np.exp(mu + 0.5 * delta ** 2) - 1)\n",
    "S = np.zeros((M + 1, I))\n",
    "S[0] = S0\n",
    "sn1 = npr.standard_normal((M + 1, I))\n",
    "sn2 = npr.standard_normal((M + 1, I))\n",
    "poi = npr.poisson(lamb * dt, (M + 1, I))\n",
    "for t in range(1, M + 1, 1):\n",
    "    S[t] = S[t - 1] * (np.exp((r - rj - 0.5 * sigma ** 2) * dt\n",
    "                       + sigma * np.sqrt(dt) * sn1[t])\n",
    "                       + (np.exp(mu + delta * sn2[t]) - 1)\n",
    "                       * poi[t])\n",
    "    S[t] = np.maximum(S[t], 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "uuid": "37cfd26e-2c44-456a-8b8b-56cf10e12aac"
   },
   "outputs": [],
   "source": [
    "R_jd = np.sort(S[-1] - S0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "uuid": "3300cad0-872b-45ef-9b12-3fc3507b2c54"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x115993518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(R_jd, bins=50)\n",
    "plt.xlabel('absolute return')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: var_hist_jd\n",
    "# title: Absolute returns of jump diffusion (30d)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "uuid": "8adcca19-77bf-4d8e-a342-1a5cc1cadd69"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence Level    Value-at-Risk\n",
      "---------------------------------\n",
      "           99.99           75.029\n",
      "           99.90           71.833\n",
      "           99.00           55.901\n",
      "           97.50           45.697\n",
      "           95.00           25.993\n",
      "           90.00            8.773\n"
     ]
    }
   ],
   "source": [
    "percs = [0.01, 0.1, 1., 2.5, 5.0, 10.0]\n",
    "var = scs.scoreatpercentile(R_jd, percs)\n",
    "print(\"%16s %16s\" % ('Confidence Level', 'Value-at-Risk'))\n",
    "print(33 * \"-\")\n",
    "for pair in zip(percs, var):\n",
    "    print(\"%16.2f %16.3f\" % (100 - pair[0], -pair[1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "uuid": "812884b3-c147-4799-8b7a-93eb62a9b1fc"
   },
   "outputs": [],
   "source": [
    "percs = list(np.arange(0.0, 10.1, 0.1))\n",
    "gbm_var = scs.scoreatpercentile(R_gbm, percs)\n",
    "jd_var = scs.scoreatpercentile(R_jd, percs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "uuid": "b960f3cc-fed3-4cfa-9189-040931e4ab09"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-90.277619106623035, 0.0)"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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2+NzscuC4hEUlK0l9fyZZN1xD2gfv0zRmLFW33E50k039DktE+rD2ag5fAyW0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\nRFr5f91HZG8AbkcMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115d35d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(percs, gbm_var, 'b', lw=1.5, label='GBM')\n",
    "plt.plot(percs, jd_var, 'r', lw=1.5, label='JD')\n",
    "plt.legend(loc=4)\n",
    "plt.xlabel('100 - confidence level [%]')\n",
    "plt.ylabel('value-at-risk')\n",
    "plt.grid(True)\n",
    "plt.ylim(ymax=0.0)\n",
    "# tag: var_comp\n",
    "# title: Value-at-risk for geometric Brownian motion and jump diffusion\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Credit Value Adjustments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "uuid": "92795f2e-84b4-4881-960f-91a39eb1cc77"
   },
   "outputs": [],
   "source": [
    "S0 = 100.\n",
    "r = 0.05\n",
    "sigma = 0.2\n",
    "T = 1.\n",
    "I = 100000\n",
    "ST = S0 * np.exp((r - 0.5 * sigma ** 2) * T \n",
    "             + sigma * np.sqrt(T) * npr.standard_normal(I))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "uuid": "3e3c6a61-c268-44f4-bce9-f3c2f83faac9"
   },
   "outputs": [],
   "source": [
    "L = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "uuid": "f06f2c7d-8c1a-4cc3-b171-dad76994c6b9"
   },
   "outputs": [],
   "source": [
    "p = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "uuid": "38b71c82-76a1-4299-992f-93820cbf2677"
   },
   "outputs": [],
   "source": [
    "D = npr.poisson(p * T, I)\n",
    "D = np.where(D > 1, 1, D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "uuid": "46418aea-2253-4f09-840a-1c45676bda2c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99.981825216842921"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(-r * T) * 1 / I * np.sum(ST)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "uuid": "fe7436d3-4eb4-40f4-9d4c-c5efa0e3d3a0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5152011134161355"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CVaR = np.exp(-r * T) * 1 / I * np.sum(L * D * ST)\n",
    "CVaR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "uuid": "3070c8f6-8a77-4373-b423-f6871170dbaf"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99.466624103426781"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S0_CVA = np.exp(-r * T) * 1 / I * np.sum((1 - L * D) * ST)\n",
    "S0_CVA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "uuid": "d7d14139-b76d-4c11-a57b-930db11abd3c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99.48479888658386"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S0_adj = S0 - CVaR\n",
    "S0_adj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "uuid": "c6995617-5021-4d8f-9f94-8fca0571ff89"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1031"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.count_nonzero(L * D * ST)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "uuid": "fc6e6717-9ffc-486c-a736-3892c277f3e6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 175)"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ahAwFSVLFUJAkVQwFSVLFUJAkVQwFSVLFUJAkVQwFSVLFUJAkVbyiWdKMZrpXhNNiDC5H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\nJFUMBUlSxVCQJFUMBUlS5f8BomgNLHxSz58AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11569c9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(L * D * ST, bins=50)\n",
    "plt.xlabel('loss')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "plt.ylim(ymax=175)\n",
    "# tag: cva_hist_stock\n",
    "# title: Losses due to risk-neutrally expected default (stock)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "uuid": "59b7c831-c915-4c06-a23b-0ac913220d76"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.427336109660052"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K = 100.\n",
    "hT = np.maximum(ST - K, 0)\n",
    "C0 = np.exp(-r * T) * 1 / I * np.sum(hT)\n",
    "C0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "uuid": "da0198e3-10bc-4324-8e0e-b09c2e61e94d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.053822578452208093"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CVaR = np.exp(-r * T) * 1 / I * np.sum(L * D * hT)\n",
    "CVaR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "uuid": "24d26328-f3f2-4da4-8d5c-7fb06a70eec8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.373513531207843"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C0_CVA = np.exp(-r * T) * 1 / I * np.sum((1 - L * D) * hT)\n",
    "C0_CVA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "uuid": "a221dbb8-eec3-45e1-abd7-146050c0285f"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "582"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.count_nonzero(L * D * hT)  # number of losses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "uuid": "e1becbb6-7a1e-49bb-8a8e-b7daab189c6e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1031"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.count_nonzero(D)  # number of defaults"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "uuid": "44c3d031-8002-4bba-abd7-0db5451b2d52"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "43995"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "I - np.count_nonzero(hT)  # zero payoff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "uuid": "b132d24e-093b-45e6-a4cc-29b8ef006038"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 350)"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a2c67b278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(L * D * hT, bins=50)\n",
    "plt.xlabel('loss')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "plt.ylim(ymax=350)\n",
    "# tag: cva_hist_opt\n",
    "# title: Losses due to risk-neutrally expected default (call option)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Further Reading"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>\n",
    "\n",
    "<a href=\"http://tpq.io\" target=\"_blank\">http://tpq.io</a> | <a href=\"http://twitter.com/dyjh\" target=\"_blank\">@dyjh</a> | <a href=\"mailto:training@tpq.io\">training@tpq.io</a>\n",
    "\n",
    "**Quant Platform** |\n",
    "<a href=\"http://quant-platform.com\">http://quant-platform.com</a>\n",
    "\n",
    "**Python for Finance** |\n",
    "<a href=\"http://python-for-finance.com\" target=\"_blank\">Python for Finance @ O'Reilly</a>\n",
    "\n",
    "**Derivatives Analytics with Python** |\n",
    "<a href=\"http://derivatives-analytics-with-python.com\" target=\"_blank\">Derivatives Analytics @ Wiley Finance</a>\n",
    "\n",
    "**Listed Volatility and Variance Derivatives** |\n",
    "<a href=\"http://lvvd.tpq.io\" target=\"_blank\">Listed VV Derivatives @ Wiley Finance</a>\n",
    "\n",
    "**Python Training** |\n",
    "<a href=\"http://training.tpq.io\" target=\"_blank\">Python for Finance University Certificate</a>"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
